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The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...
Some programming languages, e.g., Ada, have short-circuit Boolean operators. These operators use a lazy evaluation, that is, if the value of the expression can be determined from the left hand Boolean expression then they do not evaluate the right hand Boolean expression.
Sometimes used for “relation”, also used for denoting various ad hoc relations (for example, for denoting “witnessing” in the context of Rosser's trick). The fish hook is also used as strict implication by C.I.Lewis p {\displaystyle p} ⥽ q ≡ ( p → q ) {\displaystyle q\equiv \Box (p\rightarrow q)} .
For example, (a > 0 and not flag) and (a > 0 && !flag) specify the same behavior. As another example, the bitand keyword may be used to replace not only the bitwise-and operator but also the address-of operator, and it can be used to specify reference types (e.g., int bitand ref = n).
The second example shows that the exclusive inference vanishes away under downward entailing contexts. If disjunction were understood as exclusive in this example, it would leave open the possibility that some people ate both rice and beans. [4] 2. Mary is either a singer or a poet or both. 3. Nobody ate either rice or beans.
The detailed semantics of "the" ternary operator as well as its syntax differs significantly from language to language. A top level distinction from one language to another is whether the expressions permit side effects (as in most procedural languages) and whether the language provides short-circuit evaluation semantics, whereby only the selected expression is evaluated (most standard ...
A sequence of bits is a commonly used example of such a function. Another common example is the totality of subsets of a set E: to a subset F of E, one can define the indicator function that takes the value 1 on F, and 0 outside F. The most general example is the set elements of a Boolean algebra, with all of the foregoing being instances thereof.
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.